Analyzing temporally and spectrally complex signals is challenging and requires the use of specialized techniques. Such temporally and spectrally complex signals include for example biological signals (e.g. neural and cardiac signals), noisy or artifact-contaminated communication signals, signals produced by mechanical or electronic measurement or sensing devices (e.g. spectrometers, acoustic transducers etc.) and environmental signals (e.g. atmospheric, oceanic, seismic and astronomic signals). Despite the popularity of Fourier transform-based methods, such methods are ill-suited to deal with non-stationary complex signals. As an alternative, wavelet transform-based methods have proven to be versatile and effective, with improved ability to resolve complex signal features in both the time and frequency domains.
Large amplitude spikes are common features in temporally and spectrally complex signals. For example, in the case of neural signals, large amplitude spikes may occur spontaneously and/or as a byproduct of stimulation. Unfortunately, large amplitude spikes or artifacts can obscure complex signal components that are relevant to clinical/research diagnosis and/or analysis since their dominant spectral power masks smaller amplitude complex signal features that may be temporally localized at the same regions as the large amplitude spikes. If large amplitude spikes are associated with an underlying rhythm and require removal, then wavelet transform-based methods alone are not capable of eliminating all spike remnants, since spikes with large amplitudes in relation to the rest of the complex signal tend to dominate the coefficients of the wavelet transform across all frequency bands being analyzed.
For example, electroencephalogram (EEG) artifacts may originate from various physiological and external sources (e.g. eye blinking, muscular movement, cardiac potentials, etc.) and can pose difficulties for EEG analysis, as noted in the publications entitled “Methods for the estimation and removal of artifacts and overlap in ERP waveforms” authored by D. Talsma et al., Event-Related Potentials: A Methods Handbook, MIT Press, 2005, p. 115-148 and “Facts and artifacts in brain electrical activity mapping” authored by K. L. Coburn et al., Brain Topology 1, (1):37-45, 1988. In another example, isolation of the baseline complex signal in intracellular neuronal recordings is sometimes warranted due to active research into forms of subthreshold neuronal noise and their role in synaptic function and neuronal communication, making action potential attenuation or removal desirable as noted in the publications entitled “Noise in the nervous system” authored by A. A. Faisal et al., Nature Reviews Neuroscience, 9(4):292-303, 2008, “A nonrandom dynamic component in the synaptic noise of a central neuron” authored by P. Faure et al., Proceedings of the National Academy of Sciences, 94(12):6506-6511, 1997, and “Subthreshold voltage noise of rat neocortical pyramidal neurons” authored by G. Jacobson et al., Journal of Physiology, 564(Pt 1):145-160, 2005.
Several techniques have been devised to remove large amplitude spikes from complex signals. One approach involves interpolating the baseline potential of the complex signal before and after each spike following its excision, and then lowpass filtering the complex signal. Unfortunately, lowpass filtering the complex signal may remove other high-frequency components in the complex signal not associated with spike artifacts. A cruder method relies on direct bandpass filtering to attenuate dominant-frequency spike components of the complex signal, but this approach usually distorts the underlying complex signal as well.
As will be appreciated, improvements in complex signal analysis are desired. It is therefore an object of the present invention to provide a novel method and attenuator for attenuating spikes in complex signals.